The invention relates generally to efficiently coupling optical waveguides and more particularly to determining the positions and angles of waveguides relative to a plane of total internal reflection.
Increasingly, signal transfers within a telecommunications or data communications environment are being carried out using optical networks. Information can be exchanged in the form of modulations of laser-produced light. The equipment for efficiently generating optical signals and the cables for transmitting the optical signals over extended distances are readily available. However, there are still some concerns with regard to enabling localized manipulation of signals without a significant sacrifice of signal strength. The localized manipulation may be a steady-state signal transfer arrangement between two waveguides or may be a switching arrangement in which an optical signal along one waveguide can be transferred to any one of a number of output waveguides.
One technique for redirecting an optical signal from one waveguide to another waveguide is to use a mirror. The mirror may be stationary or may be used in a switching arrangement by connecting the mirror to a micromachine device. An alternative to using the mirror is to provide a plane of total internal reflection (TIR). As is known in the art, TIR occurs when a ray of light travels toward an interface between a region having a high refractive index and a region of low refractive index, with the ray of light approaching from the high index side of the interface. A switching arrangement that utilizes the phenomenon of TIR is described in U.S. Pat. No. 5,699,462 to Fouquet et al., which is assigned to the assignee of the present invention. An isolated switching unit 10 is shown in FIG. 1. The switching unit includes planar waveguides that are formed by layers on a substrate. The waveguide layers include a lower cladding layer 14, an optical core 16, and an upper cladding layer, not shown. The optical core may be primarily silicon dioxide, but with doping materials that achieve a desired index of refraction. The cladding layers are formed of a material having a refractive index that is significantly different than that of the core material, so that the optical signals are guided along the core. The effective phase index of the waveguide is determined by the refractive indices of the core material and the material of the cladding layers, as is well known in the art. The layer of core material is patterned into waveguide segments that define a first input waveguide 20 and a first output waveguide 26 of a first optical path. The patterning also defines a second input waveguide 24 and a second output waveguide 22 of a second linear path. The upper cladding layer is then deposited over the patterned core material. A gap is formed by etching a trench 28 through the core material, the upper cladding layer, and at least a portion of the lower cladding layer 14.
The first input waveguide 20 and the second output waveguide 22 have axes that intersect a sidewall of the trench 28 at an angle of incidence that results in TIR diverting light from the input waveguide 20 to the output waveguide 22 when the junction 30 of the waveguides is filled with vapor or gas. However, when the junction 30 is filled with a fluid that has an index of refraction substantially matching that of the effective phase index of the waveguides, light from the input waveguide 20 will travel through the index-matching fluid to the linearly aligned first output waveguide 26.
The patent to Fouquet et al. describes a number of alternative embodiments to switching the optical switching unit 10 between a transmitting state and reflecting state. In the transmitting state, the two input waveguides 20 and 24 are optically coupled to their linearly aligned output waveguides 26 and 22, respectively. In the reflecting state, the first input waveguide 20 is optically coupled to the second output waveguide 22, but the second input waveguide 24 is not in communication with either of the output waveguides 22 and 26. One approach to switching between the two states is illustrated in FIG. 1. The switching unit 10 includes a microheater 38 that controls formation of a bubble within the fluid-containing trench. When the heater is brought to a temperature that is sufficiently high to form a bubble in the index-matching fluid, the bubble is positioned at the junction 30 of the four waveguides. Consequently, light propagating along the waveguide 20 encounters a refractive index mismatch upon reaching the sidewall of the trench 28, causing TIR, so that the waveguides 20 and 22 are optically coupled. However, when the heater 38 is deactivated, the index-matching fluid will again reside within the junction between the four waveguides.
The principles described with reference to FIG. 1 also apply to a steady-state reflecting arrangement. That is, if the index-matching fluid is removed from the trench 28, the waveguides 20 and 22 will be continuously coupled by TIR at the wall of the trench. In this steady-state embodiment, the waveguides 24 and 26 would not be included.
While the phenomenon of TIR has been used successfully in the redirection of optical signals from one waveguide to another waveguide, further improvements are desired. Light that impinges an interface between a high refractive index region and a low refractive index region will vary between having a transverse electric (TE) polarization and having a transverse magnetic (TM) polarization. The light will react differently at the interface, depending upon its polarization. Consequently, there are polarization dependent losses (PDLs) due to imperfect coupling to the waveguide modes. Since light impinging the interface will randomly vary between polarizations, the variations in PDL are random.
What is needed is an optical coupling arrangement of waveguides in which polarization dependent losses are neutralized or rendered predictable. What is also needed is a method of determining efficient layouts for positioning waveguides relative to a TIR interface.
Optical efficiency in the coupling of two waveguides that intersect an interface between high and low refractive index regions is enhanced by determining compensation for the Goos-Hxc3xa4nchen effect along the interface. In one embodiment, the lateral shift of reflected light along the interface is predicted in order to determine a distance at which the axes of the two waveguides should be spaced apart along the interface. In another embodiment, the incidence angles of the two waveguides are selected so as to equalize the lateral shifts for the polarizations, since light collection by the second waveguide can be increased by selection of the proper angle, even if the spacing between the two waveguide axes remains fixed. In the preferred embodiment, both the distance between the axes and the incidence angles are selected to provide compensation for the Goos-Hxc3xa4nchen effect.
As previously noted, TIR occurs when a ray of light impinges the interface between the high and low refractive index regions from the high index side. However, the Goos-Hxc3xa4nchen effect causes the reflected light to emerge from the interface a short distance away from the point at which the incident light intersects the interface. By tailoring the positions and/or the angles of waveguides to maximize the collection of the reflected light, the reliability of signal processing can be improved. The optimal positioning is polarization dependent. That is, the lateral shift (zTM) of light having a TM polarization is different than the lateral shift (zTE) of light having a TE polarization. Reflection can be optimized for either the TM polarization or the TE polarization. Alternatively, the distance between the axes of the waveguides along the interface can be selected to equalize the loss for the two polarizations. By selecting the distance to be one-half of the difference between the two optimal points of the two polarizations, a zero-polarization dependent loss (PDL) for the reflection can be approached. This provides an acceptable overall low loss arrangement.
The lateral shift of light having the TM polarization may be calculated on the basis of the following equation:
zTM=2(N2xe2x88x92ns2)xe2x88x92xc2xd tan(xcex8)/k(N2/ns2+N2/nf2xe2x88x921)xe2x80x83xe2x80x83Eq. 1
where k=2xcfx80/xcex, ns is the low refractive index, nf is the high refractive index, N=n sine xcex8, xcex8 is the angle of incidence, and xcex is the wavelength of the light. The lateral shift for light having the TE polarization may be determined using the following equation:
zTE=2(N2xe2x88x92ns2)xe2x88x92xc2xd tan(xcex8)/kxe2x80x83xe2x80x83Eq. 2
The zTM and zTE values can be converted using known trigonometric relations to a beam displacement from the position that the beam would be obtained if a geometrical reflection were to have occurred. The conversion can be used to determine the signal attenuation that would occur if two waveguides were at geometrical reflection positions. However, the loss can be eliminated by arranging the two waveguides to intersect the plane of total internal reflection such that the axes of the waveguides are spaced apart by the desired distance. This step of arranging the waveguides may be performed by fabricating the waveguides to end at a preselected plane that defines the interface. Alternatively, the waveguides can be fabricated to have intersecting axes, but then truncating along the plane that provides the desired spacing between the two axes. As previously noted, the spacing may be selected based solely upon the determination of zTM, or solely upon the determination of zTE, or upon the average between zTM and zTE.
The incidence angles for a particular application of folding a beam path that includes propagation along two waveguides can be selected to minimize polarization dependent loss. Since the lateral shifts of Eq. 1 and Eq. 2 are dependent upon the incidence angle (xcex8), the selection of the equal angles of incidence of the two waveguides relative to the normal of the interface is a function of the refractive index (nf) of the waveguides (i.e., the effective phase index of the waveguides) and the refractive index (n2) of the region on a side of the interface opposite to the waveguides. Solving Eq. 1 and Eq. 2 for the condition that provides a substantially equal shift for the two polarizations provides the alternative equations:
sine(xcex8)=(2/(nf2/ns2+1))xc2xdxe2x80x83xe2x80x83Eq. 3
and
xcex8=arcsine((2/(nf2/ns2+1))xc2xd)xe2x80x83xe2x80x83Eq. 4
Similar to the determination of axial displacement along the interface, the incidence angle can be optimized for one polarization or the other, but Eq. 4 is preferably used to determine the condition in which the polarization dependent loss is theoretically zero. As one example of an implementation, if ns is the refractive index of air and the waveguides are formed of materials that provide an effective phase index (nf) in the range of 1.30 to 1.60, the range of incidence angles determined using Eq. 4 will be 48xc2x0 to 60xc2x0.